Two weeks after the Democrats’ historic, 26-hour sit-in demanding House votes on gun control legislation, Democrats have kept their drumbeat alive on the House floor, while advocates have held parallel events outside the chambers.

To get a vote, part of Connecticut congressman John Larson’s strategy has been to put some trust in House speaker Paul Ryan. Larson, one of the organizers of the sit-in, met privately with Ryan and congressman John Lewis on Tuesday night.

The meeting ended without a deal on a vote for Democratic gun bills. But Larson said his faith in Ryan led him to convince members of his party to support a mental health bill that passed by an almost unanimous vote Wednesday, in hopes that Democratic support of a bipartisan bill might appeal to the “better angels” of the Republican party – and influence Ryan to advance a gun vote.

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Democrats had discussed opposing the mental health bill, according to Larson. Some members of the Democratic caucus were concerned Republicans would use their passage of mental health legislation as evidence they were addressing America’s mass shooting problem, despite a refusal to hold even a single vote on strengthening the country’s gun laws. Democrats were also concerned that the bill might be “rammed through” without much discussion, Larson said.

But during the Tuesday meeting with Ryan and Lewis, who also led the sit-ins, Ryan asked the lawmakers about rumors that Democrats were planning to torpedo a planned vote on the mental health bill.

Ryan never promised to facilitate a vote on gun reform in exchange for Democrats’ support on the bill. But after Larson and Lewis left the meeting, he said, their caucus decided to make a “good faith” to move forward with the mental health legislation.

The mental health bill, sponsored by Republican congressman Tim Murphy, passed the House on Wednesday afternoon by an almost unanimous vote, and was hailed as an important step forward by the National Alliance on Mental Illness.

“We thought this would demonstrate that in the midst of our disagreements we can still accomplish something that’s important,” Larson said in an interview before the vote on Wednesday afternoon. In turn, Larson said, he hoped Republicans “would see fit to grant us a vote” on gun control bills.

“Paul never said, ‘Oh, here if you do this …’ He never made any deal. He mentioned it. So we think it’s the right thing to do, and we hope it appeals to their better angels.

“We thought this would demonstrate that in the midst of our disagreements we can still accomplish something that’s important,” Larson said.

By relying on the higher feelings of House Republicans to get a gun control vote, Larson said, “I guess we run the risk of being called naive.”

In a radio interview Tuesday, Ryan addressed the Democrats’ push for gun control votes by saying: “Win elections and get the majority, then you can set the agenda,” a remark widely interpreted to mean that Democrats would not be seeing any votes on their gun control legislation this year.

But when Larson asked Ryan about these comments, he said, “he just kind of looked at us, in, you know, he didn’t say anything”.

That left Larson with the impression that a vote on Democratic gun control bills, if not likely, might be possible. Larson said he had been warned going into the meeting that Ryan would lecture them that if they wanted to hold a vote on their bills they would have to win an election. That’s not what happened, he said.

“I think he was sincerely listening. Does that meant he’s going to act in our favor? No.”

House Democrats are currently pushing two bills: one that would bar suspected terrorists from buying guns, and one that would expand background checks to private sales at gun shows and over the internet.

Republicans have agreed to only a single gun-related vote, on a measure that would give law enforcement officials three days to delay the purchase of a gun by a suspected terrorist, and then convince a judge to block the sale. Democrats have called the measure, which is similar to a Senate measure approved by the National Rifle Association, a “cynical” and unworkable policy which would not make Americans safer. Republicans and some on the left both argue that a more aggressive policy to block suspected terrorists from buying guns would violate due process.

When they asked Ryan if he might support Republican senator Susan Collins’ compromise legislation to bar suspected terrorists from buying guns, Ryan “said ‘I’m for due process.’ He did not tie himself down to specifics,” Larson said.

Larson said he thinks the speaker is an “honorable guy” and that he listened seriously to what Lewis had to say and “took it to heart”.

House Democrats cannot even hold a vote on their legislation without approval of Republicans. As Democrats have seen an enthusiastic public response to their sit-in, Larson said, “There’s more outside pressure than we can exert inside. On the inside, they’re the majority, and they control, through the rules’ committee, the process – the process that has seen us without a vote over 3.5 years since Sandy Hook.”

The Connecticut congressman said that Democrats have “a list of things that people are going to do as we go forward” to reassure their supporters that “we’re not going anywhere” on the gun issue. Both more restrained and more escalated tactics are on the list. He would not provide details. Democrats are regrouping for frequent strategy sessions in the officers of Jim Clyburn and Democratic whip StenyHoyer.

Even though members of Congress have drawn back this week from passionate civil disobedience to color-inside-the-lines protests and press conferences, Larson said he still feels that Democrats have energetic support from their constituents – as well as internal discipline to stay focused on the two gun control bills.

“I don’t belong to any organized party. I’m a Democrat,” he quipped. “I’ve never seen us as unified and people disciplined, coming to the floor, talking about these two issues.”